$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 7x + 7$ and $ JT = 4x + 25$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {7x + 7} = {4x + 25}$ Solve for $x$ $ 3x = 18$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 7({6}) + 7$ $ JT = 4({6}) + 25$ $ CJ = 42 + 7$ $ JT = 24 + 25$ $ CJ = 49$ $ JT = 49$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {49} + {49}$ $ CT = 98$